Lecture 8 Testability Measures

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Lecture 8Testability Measures

• Origins
• Controllability and observability
• SCOAP measures
• Sources of correlation error
• Combinational circuit example
• Sequential circuit example
• Test vector length prediction
• High-Level testability measures
• Summary

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Purpose

• Need approximate measure of
• Difficulty of setting internal circuit lines to 0
  or 1 by setting primary circuit inputs
• Difficulty of observing internal circuit lines by
  observing primary outputs
• Uses
• Analysis of difficulty of testing internal
  circuit parts redesign or add special test
  hardware
• Guidance for algorithms computing test patterns
  avoid using hard-to-control lines
• Estimation of fault coverage
• Estimation of test vector length

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Origins

• Control theory
• Rutman 1972 -- First definition of
  controllability
• Goldstein 1979 -- SCOAP
• First definition of observability
• First elegant formulation
• First efficient algorithm to compute
  controllability and observability
• Parker McCluskey 1975
• Definition of Probabilistic Controllability
• Algebraic method to compute line
  controllabilities
• Brglez 1984 -- COP
• 1st probabilistic measures
• Seth, Pan Agrawal 1985 PREDICT
• 1st exact probabilistic measures

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Probabilistic Testability Measure

• Overcome limitations of SCOAP
• Related to signal probabilities
• 1-controllability (C1) ? the probability of a
  signal value on line l being set to 1 by a random
  vector
• 0-controllability (C0) ? the probability of a
  signal value on line l being set to 0 by a
  random vector

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Seth and Agrawal

• Break a circuit into sub-circuits, called
  supergates
• Supergate completely include reconvergent
  fanouts
• Worst case, the entire circuit may be a supergate
• Computes exact probabilities
• Computational complexity is exponential with the
  circuit size
• Several heuristics were developed to reduce
  run-time

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Fault Detection Probability

• 1-controllability of a signal that is the XOR of
  the good and faulty circuit outputs
• Observability of line l OB(l) the probability of
  sensitizing a path from l to a PO
• Detecting a Stuck-at-0 at line l ! C1(l)xOB(l) ?
  controllability and observability is not
  independent!

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Testability Analysis

• Involves Circuit Topological analysis, but no
• test vectors and no search algorithm
• Static analysis
• Linear computational complexity
• Otherwise, is pointless might as well use
• automatic test-pattern generation and
• calculate
• Exact fault coverage
• Exact test vectors

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Types of Measures

• SCOAP Sandia Controllability and Observability
  Analysis Program
• Combinational measures
• CC0 Difficulty of setting circuit line to logic
  0
• CC1 Difficulty of setting circuit line to logic
  1
• CO Difficulty of observing a circuit line
• Sequential measures analogous
• SC0
• SC1
• SO

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Range of SCOAP Measures

• Controllabilities 1 (easiest) to infinity
  (hardest)
• Observabilities 0 (easiest) to infinity
  (hardest)
• Combinational measures
• Roughly proportional to circuit lines that must
  be set to control or observe given line
• Sequential measures
• Roughly proportional to times a flip-flop must
  be clocked to control or observe given line

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Goldsteins SCOAP Measures

• AND gate O/P 0 controllability
• output_controllability min
  (input_controllabilities)
• 1
• AND gate O/P 1 controllability
• output_controllability S (input_controllabili
  ties)
• 1
• XOR gate O/P controllability
• output_controllability min (controllabilities
  of
• each input
  set) 1
• Fanout Stem observability
• S or min (some or all fanout branch
  observabilities)

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Controllability Examples
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More ControllabilityExamples
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Observability Examples
To observe a gate input Observe output and make
other input values non-controlling
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More Observability Examples

• To observe a fanout stem
• Observe it through branch with best observability

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Error Due to Stems Reconverging Fanouts

• SCOAP measures wrongly assume that controlling or
  observing x, y, z are independent events
• CC0 (x), CC0 (y), CC0 (z) correlate
• CC1 (x), CC1 (y), CC1 (z) correlate
• CO (x), CO (y), CO (z) correlate

x
y
z
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Correlation Error Example

• Exact computation of measures is NP-Complete and
  impractical
• Italicized (green) measures show correct values
  SCOAP measures are in red or bold CC0,CC1 (CO)

2,3(4) 2,3(4, )
1,1(6) 1,1(5, )
x
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6,2(0) 4,2(0)
8
(6)
(5) (4,6)
y
1,1(5) 1,1(4,6)
2,3(4) 2,3(4, )
(6)
z
8
1,1(6) 1,1(5, )
8
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Sequential Example
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Levelization Algorithm 6.1

• Label each gate with max of logic levels from
  primary inputs or with max of logic levels from
  primary output
• Assign level 0 to all primary inputs (PIs)
• For each PI fanout
• Label that line with the PI level number,
• Queue logic gate driven by that fanout
• While queue is not empty
• Dequeue next logic gate
• If all gate inputs have level s, label the gate
  with the maximum of them 1
• Else, requeue the gate

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Controllability Through Level 0
Circled numbers give level number. (CC0, CC1)
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Controllability Through Level 2
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Final Combinational Controllability
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Combinational Observability for Level 1
Number in square box is level from primary
outputs (POs). (CC0, CC1) CO
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Combinational Observabilities for Level 2
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Final Combinational Observabilities
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Sequential Measure Differences

• Combinational
• Increment CC0, CC1, CO whenever you pass through
  a gate, either forwards or backwards
• Sequential
• Increment SC0, SC1, SO only when you pass through
  a flip-flop, either forwards or backwards, to Q,
  Q, D, C, SET, or RESET
• Both
• Must iterate on feedback loops until
  controllabilities stabilize

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D Flip-Flop Equations

• Assume a synchronous RESET line.
• CC1 (Q) CC1 (D) CC1 (C) CC0 (C) CC0
• (RESET)
• SC1 (Q) SC1 (D) SC1 (C) SC0 (C) SC0
• (RESET) 1
• CC0 (Q) min CC1 (RESET) CC1 (C) CC0 (C),
• CC0 (D) CC1 (C) CC0 (C)
• SC0 (Q) is analogous
• CO (D) CO (Q) CC1 (C) CC0 (C) CC0
• (RESET)
• SO (D) is analogous

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D Flip-Flop Clock and Reset

• CO (RESET) CO (Q) CC1 (Q) CC1 (RESET)
• CC1 (C) CC0 (C)
• SO (RESET) is analogous
• Three ways to observe the clock line
• Set Q to 1 and clock in a 0 from D
• Set the flip-flop and then reset it
• Reset the flip-flop and clock in a 1 from D
• CO (C) min CO (Q) CC1 (Q) CC0 (D)
  
• CC1 (C) CC0 (C),
• CO (Q) CC1 (Q)
  CC1 (RESET)
• CC1 (C) CC0 (C),
• CO (Q) CC0 (Q)
  CC0 (RESET)
• CC1 (D) CC1 (C)
  CC0 (C)
• SO (C) is analogous

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Algorithm 6.2Testability Computation

• For all PIs, CC0 CC1 1 and SC0 SC1 0
• For all other nodes, CC0 CC1 SC0 SC1
• Go from PIs to POS, using CC and SC equations to
  get controllabilities -- Iterate on loops until
  SC stabilizes -- convergence guaranteed
• For all POs, set CO SO
• Work from POs to PIs, Use CO, SO, and
  controllabilities to get observabilities
• Fanout stem (CO, SO) min branch (CO, SO)
• If a CC or SC (CO or SO) is , that node is
  uncontrollable (unobservable)

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Sequential Example Initialization
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After 1 Iteration
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After 2 Iterations
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After 3 Iterations
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Stable Sequential Measures
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Final Sequential Observabilities
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Test Vector Length Prediction

• First compute testabilities for stuck-at faults
• T (x sa0) CC1 (x) CO (x)
• T (x sa1) CC0 (x) CO (x)
• Testability index log S T (f i)

fi
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Number Test Vectors vs. Testability Index
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High Level Testability

• Build data path control graph (DPCG) for circuit
• Compute sequential depth -- arcs along path
• between PIs, registers, and POs
• Improve Register Transfer Level Testability with
  
• redesign

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Improved RTL Design
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Summary

• Testability approximately measures
• Difficulty of setting circuit lines to 0 or 1
• Difficulty of observing internal circuit lines
• Uses
• Analysis of difficulty of testing internal
  circuit parts
• Redesign circuit hardware or add special test
  hardware where measures show bad controllability
  or observability
• Guidance for algorithms computing test patterns
  avoid using hard-to-control lines
• Estimation of fault coverage 3-5 error
• Estimation of test vector length